Pascal's principle
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Pascal's principle says that if you squeeze an enclosed fluid at one spot, that extra pressure is felt everywhere throughout the fluid, undiminished. Press the plunger of a full, capped water bottle and every part of the water inside feels the same added push at once. It answers the question: when you increase the pressure at one place in a trapped liquid, where does that pressure go?
Precisely, Pascal's principle states that a change in pressure applied to an enclosed, incompressible fluid is transmitted equally to every point of the fluid and to the walls of its container. In symbols, the pressure increase delta P added at one location appears as the same delta P at every other location. This works because a liquid barely compresses, so a push at one end cannot be absorbed by shrinking; it must be passed along to everything the fluid touches.
This principle is the beating heart of hydraulics: car brakes, the lifts in a garage, and the great forces of a hydraulic press all rely on it. One honest condition to remember: the principle is about the change in pressure, added on top of whatever pressure the fluid already had (including the pressure differences from depth). It also assumes the fluid is enclosed and effectively incompressible, which is why hydraulic systems use oil or water rather than easily squashed air.
Squeeze one end of a sealed, water-filled tube and a piston at the far end pushes out with the same added pressure, no matter how long or bent the tube is, because the pressure change travels through the whole liquid.
A pressure change added anywhere in a trapped liquid reaches everywhere in it equally.
Pascal's principle concerns the transmitted change in pressure and assumes an enclosed, nearly incompressible fluid; it does not erase the pressure differences that already exist due to depth.